Pop star Gary Barlow has finally broken his silence to apologise after damaging tax avoidance allegations. The multimillionaire former Take That singer-songwriter was accused earlier this year of being involved in an "aggressive" tax avoidance scheme.

Barlow, a prolific tweeter, refused to comment after coming under a deluge of criticism. Some called for him to be stripped of his OBE when the story broke in May. Barlow, 43, was awarded his OBE by the Queen in November 2012.

But last night Barlow, a Tory supporter who lives in the constituency of the prime minister spoke for the first time, about his tax affairs with two posts on his Twitter account. He said: "I want to apologise to anyone who was offended by the tax stories earlier this year." A second tweet said: "With a new team of accountants, we are working to settle things with all parties involved ASAP."

Minutes later, he tweeted the news to his 3.5 million followers that he had been working on a new Take That album and a Broadway musical. He did not elaborate further on his tax arrangements.

He had earlier tweeted that he had just come back from "Seven productive weeks in the US" and had taken a break from Twitter after his account was hacked and "some very upsetting and disturbing text was written."

David Cameron rejected calls for Barlow to hand back his OBE after the star was ordered in May to pay millions of pounds in tax that had gone unpaid because of an avoidance scheme. The prime minister said it was not "necessary" to remove Barlow's honour because he had "raised money for charity". The defence came despite Cameron having previously condemned comedian Jimmy Carr for investing in a similar tax scheme. But Labour's Margaret Hodge, chair of the Public Accounts Committee, said Barlow should hand back his OBE, and the Liberal Democrat chief secretary to the Treasury, Danny Alexander, said: "People who don't pay the taxes that they should undermine the economy, damage our public services and place an extra, unfair burden on hardworking families and companies who play by the rules."

Barlow and two other members of Take That have refused to comment on reports that they are in line for tax bills totalling tens of millions of pounds after a court ruled a partnership in which they invested was a tax avoidance scheme.

The singer, with Howard Donald, Mark Owen and their manager Jonathan Wild, reportedly invested £66m into two partnerships styled as music industry investment schemes. Judge Colin Bishopp ruled that 51 partnerships set up by Icebreaker Management were to secure tax relief for members and HM Revenue and Customs is now expected to demand repayment.

It was alleged in 2012 that Barlow, Donald, Owen and Wild invested at least £26m in a scheme run by Icebreaker Management. At the time, Take That's lawyers insisted that the bandmates believed the investments were legitimate enterprises and that all four named paid "significant tax".

Barlow masterminded the Queen's diamond jubilee concert, which was staged at Buckingham Palace during a special bank holiday weekend in June 2012.

A Sky News video showed the PM telling two Take That fans: "He lives in my constituency in West Oxfordshire... He is such a nice man."